Half is a third of it. what is it?

Let's call 'it' x. 1/2 is equal to one third of x, so we could say that 1/3x = 1/2

Now we just have a simple equation to solve:

1/3x = 1/2
x = (1/2) / (1/3)

Dividing by a rational number (such as 1/3, which is expressed in fraction form) is the same as multiplying by its reciprocal (the reciprocal of a fraction is itself when the numerator and denominator have been swapped). Therefore

x = (1/2) / (1/3) = (1/2) * 3 = 3/2 = 1.5

To check this answer, test the statement. Half is a third of x, where x=1.5:

1.5 / 3 = 0.5 = 1/2

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